In a circle with radius 5.1, an angle intercepts an arc of length 30.3. Find the angle in radians to the nearest 10th.

Question

In a circle with radius 5.1, an angle intercepts an arc of length 30.3. Find the angle in
radians to the nearest 10th.

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Nguyệt Ánh 1 year 2021-07-19T07:18:53+00:00 1 Answers 20 views 0

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    2021-07-19T07:20:34+00:00

    Answer:

    5.9 radian

    Step-by-step explanation:

    Applying,

    S = 2πrФ/360°…………….. Equation 1

    Where s = length of the arc, r = radius, Ф = angle.

    make Ф the subject of the equation

    Ф = 360S/(2πr)……….. Equation 2

    From the question,

    Given: S = 30.3, r = 5.1

    Constant: π = 3.14

    Substitute into equation 2

    Ф = (360×30.3)/(2×5.1×3.14)

    Ф = 340.58°

    Ф = (340.58×2×3.14)/360

    Ф = 5.9 radian

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